Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper we present a new approach to solving a one-dimensional, one-phase Stefan problem. The proposed method is based on choosing (a) suitable curvilinear space coordinate/s for the heat-flow equation and the finite difference method. In the final part of this paper, examples of numerical calculations are shown.
Słowa kluczowe
Rocznik
Tom
Strony
9--14
Opis fizyczny
Bibliogr. 14 poz., rys.
Twórcy
autor
- Institute of Mathematics, Czestochowa University of Technology, Czestochowa, Poland, marek.blasik@im.pcz.pl
Bibliografia
- [1] Stefan J., Ueber einige Probleme der Theorie der Waermeleitung, S.-B. Wien. Akad. Mat. Natur. 1889, 98,173-184.
- [2] Crank J., Free and Moving Boundary Problems, Clarendon Press, Oxford 1984, 163-168.
- [3] Gupta S.C., The Classical Stefan Problem. Basic Concepts, Modeling and Analysis, Elsevier, Amsterdam 2003.
- [4] Schniewind J., Solution of the solidification problem of a one - dimensional medium by a new numerical method, The extent Journal of the Iron and Steel Institute 1963, July.
- [5] Mochnacki B., Suchy J.S., Modelowanie i symulacja krzepnięcia odlewów, WN PWN, Warszawa 1993.
- [6] Douglas J., Gallie T.M., On the numerical integration of a parabolic differential equation subject to a moving boundary condition, Duke Mathematical Journal 1955, 22, 557-571.
- [7] Murray W.D., Landis F., Numerical and machine solutions of transient heat-conduction problems involving melting or freezing, J. Heat Transfer 1959, 81, 106-12.
- [8] Crank J., The Mathematics of Diffusion, Clarendon Press, Oxford 1975.
- [9] Landau H.G., Heat conduction in a melting solid, Quarterly of Applied Mathematics 1950, 8, 81-94.
- [10] Wu Z., Luo J., Feng J., A novel algorithm for solving the classical Stefan problem, Thermal Science 2011, 15, 39-44.
- [11] Liu Junyi, Xu Mingyu, An exact solution to the moving boundary problem with fractional anomalous diffusion in drug release devices, Z. Angew. Math. Mech. (ZAMM) 2004, 84, 22-28.
- [12] Liu Junyi, Xu Mingyu, Some exact solutions to Stefan problems with fractional differential equations, J. Math. Anal. Appl. 2009, 351, 536-542.
- [13] Chen Yin, Xicheng Li, Anomalous diffusion of drug release from slab matrix: Fractional diffusion models, Int. J. Pharmaceutics 2011, 418, 78-87.
- [14] Voller V., An exact solution of a limit case Stefan problem governed by a fractional diffusion equation, Int. J. Heat Mass Transfer 2010, 53, 5622-5625.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPC6-0023-0002